Remember Kyle from the Expressions for the Product of a Number and a Sum Concept? Well, he wrote a numerical expression for the situation at the science museum, but he didn't evaluate it, which means that he doesn't have an answer to his teacher's question about cost.

Here is what Kyle wrote.

\begin{align*}22(8.95 + 2.00)\end{align*}

But there was more to the problem. Kyle also needed to figure out additional costs.

Kyle knows that there is a way to solve this with the Distributive Property, but he can’t remember exactly what to do.

In this Concept, you will learn how to use the Distributive Property to evaluate numerical expressions. Then we'll revisit this problem.

Guidance

Previously we worked on how to write numerical expressions, and now you are going to learn how to evaluate those expressions.

What does the word “evaluate” mean?

When we
evaluate
an expression, we figure out the value of that expression or the quantity of the expression.

When we evaluate expressions that have a product and a sum, we use a
property
called the Distributive Property.

What is the Distributive Property?

The Distributive Property
is a property that is a true statement about how to multiply a number with a sum. Multiply the number outside the parentheses with each number inside the parentheses. Then figure out the sum of those products.

In other words, we distribute the number outside the parentheses with both of the values inside the parentheses and find the sum of those numbers.

Let’s see how this works.

@$\begin{align*}4(3 + 2)\end{align*}@$

To use the Distributive Property, we take the four and multiply it by both of the numbers inside the parentheses. Then we find the sum of those products.

@$$\begin{align*}& 4(3) + 4(2) \\
& 12 + 8 \\
& 20\end{align*}@$$

Our answer is 20.

Here is another one.

@$\begin{align*}8(9 + 4)\end{align*}@$

Multiply the eight times both of the numbers inside the parentheses. Then find the sum of the products.

@$$\begin{align*}& 8(9) + 8(4) \\
& 72 + 32 \\
& 104\end{align*}@$$

Our answer is 104.

Now it is your turn. Evaluate these expressions using the Distributive Property.

Example A

@$\begin{align*}5(6 + 3)\end{align*}@$

Solution: 45

Example B

@$\begin{align*}2(8 + 1)\end{align*}@$

Solution: 18

Example C

@$\begin{align*}12(3 + 2)\end{align*}@$

Solution: 60

Now we can take the expression that Kyle wrote and use the Distributive Property to figure out the total amount of money needed for the trip.